Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions

Research output: Contribution to journalArticle

Abstract

Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)10.1103/PhysRev.102.1189], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)10.1103/PhysRevB.78.041101], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.

Original languageEnglish (US)
Article number226401
JournalPhysical review letters
Volume122
Issue number22
DOIs
StatePublished - Jun 4 2019

Fingerprint

wave functions
orbitals
many body problem
ground state
symmetry
configurations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions. / Luo, Di; Clark, Bryan K.

In: Physical review letters, Vol. 122, No. 22, 226401, 04.06.2019.

Research output: Contribution to journalArticle

@article{e6d314b600594b69827cd4a5e8236bc4,
title = "Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions",
abstract = "Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)10.1103/PhysRev.102.1189], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)10.1103/PhysRevB.78.041101], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.",
author = "Di Luo and Clark, {Bryan K.}",
year = "2019",
month = "6",
day = "4",
doi = "10.1103/PhysRevLett.122.226401",
language = "English (US)",
volume = "122",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "22",

}

TY - JOUR

T1 - Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions

AU - Luo, Di

AU - Clark, Bryan K.

PY - 2019/6/4

Y1 - 2019/6/4

N2 - Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)10.1103/PhysRev.102.1189], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)10.1103/PhysRevB.78.041101], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.

AB - Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)10.1103/PhysRev.102.1189], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)10.1103/PhysRevB.78.041101], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.

UR - http://www.scopus.com/inward/record.url?scp=85066961403&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066961403&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.122.226401

DO - 10.1103/PhysRevLett.122.226401

M3 - Article

C2 - 31283262

AN - SCOPUS:85066961403

VL - 122

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 22

M1 - 226401

ER -